Chapter 5 Finance HW Solutions PDF

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Chapter 5, Question 1 Wii Brothers, a game manufacturer, has a new idea for an adventure game. It can market the game either as a traditional board game or as an interactive DVD, but not both. Consider the following cash flows of the two mutually exclusive projects for the company. Assume the discount rate is 10 percent. Board Game

Year 0

–$

1,60 0

1

770

2

1,35 0

3

290

DVD – $

3,50 0 2,15 0 1,65 0 1,20 0

a. What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) b.What is the NPV for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) c. What is the IRR for each project? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) d.What is the incremental IRR? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. a.

The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment. Board game:

Cumulative cash flows Year 1 = $770 = $770 Cumulative cash flows Year 2 = $770 + 1,350 = $2,120 Payback period = 1 + ($1,350 – 770)/$1,350 Payback period = 1.61 years DVD: Cumulative cash flows Year 1 = $2,150 = $2,150 Cumulative cash flows Year 2 = $2,150 + 1,650 = $3,800 Payback period = 1 + ($3,500 – 2,150)/$1,650 Payback period = 1.82 years Since the board game has a shorter payback period than the DVD project, the company should choose the board game. b.

The NPV is the sum of the present value of the cash flows from the project, so the NPV of each project will be: Board game: NPV = –$1,600 + $770/1.10 + $1,350/1.102 + $290/1.103 NPV = $433.58 DVD: NPV = –$3,500 + $2,150/1.10 + $1,650/1.102 + $1,200/1.103 NPV = $719.76 Since the NPV of the DVD is greater than the NPV of the board game, choose the DVD. c.

The IRR is the interest rate that makes the NPV of a project equal to zero. So, the IRR of each project is:

Board game: 0 = –$1,600 + $770/(1 + IRR) + $1,350/(1 + IRR)2 + $290/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 26.30% DVD: 0 = –$3,500 + $2,150/(1 + IRR) + $1,650/(1 + IRR)2 + $1,200/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 22.65% Since the IRR of the board game is greater than the IRR of the DVD, IRR implies we choose the board game. Note that this is the choice when evaluating only the IRR of each project. The IRR decision rule is flawed because there is a scale problem. That is, the DVD has a greater initial investment than does the board game. This problem is corrected by calculating the IRR of the incremental cash flows, or by evaluating the NPV of each project. d.

To calculate the incremental IRR, we subtract the smaller project’s cash flows from the larger project’s cash flows. In this case, we subtract the board game cash flows from the DVD cash flows. The incremental IRR is the IRR of these incremental cash flows. So, the incremental cash flows of the DVD are:

D V

Year 0 Year 1 Year 2 Year 3 –$ 3,50 $ 2,15 $1,6 $1,2 0 0 50 00

D B o ar d – g a m e D V D – B o ar d g a m e

1,60 0

–$

1,90 0

$

770

1,35 0

290

1,38 0

$30 0

$91 0

Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is: 0 = C0 + C1/(1 + IRR) + C2/(1 + IRR)2 + C3/(1 + IRR)3 0 = –$1,900 + $1,380/(1 + IRR) + $300/(1 + IRR)2 + $910/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: Incremental IRR = 19.43% For investing-type projects, accept the larger project when the incremental IRR is greater than the discount rate. Since the incremental incremental IRR, 19.43 percent, is greater than the required rate of return of 10 percent, choose the DVD project.

Calculator Solution: b.

Board game CFo C01 F01 C02 F02 C03 F03 I = 10% NPV CPT $433.58

–$1,600 $770 1 $1,350 1 $290 1

DVD CFo C01 F01 C02 F02 C03 F03 I = 10% NPV CPT $719.76

–$3,500 $2,150 1 $1,650 1 $1,200 1

c.

Board game CFo C01 F01 C02 F02 C03 F03 IRR CPT 26.30%

–$1,600 $770 1 $1,350 1 $290 1

d.

Incremental cash flows CFo –$1,900 C01 $1,380 F01 1 C02 $300 F02 1 C03 $910 F03 1 IRR CPT 19.43%

Chapter 5, Question 2

DVD CFo C01 F01 C02 F02 C03 F03 IRR CPT 22.65%

–$3,500 $2,150 1 $1,650 1 $1,200 1

Consider the following cash flows of two mutually exclusive projects for AZMotorcars. Assume the discount rate for both projects is 9 percent. Year 0 1 2 3

AZM AZF Mini-SUV Full-SUV 460,00 – 810,00 –$ 0 $ 0 322,00 352,00 0 0 184,00 424,00 0 0 152,00 292,00 0 0

a. What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

b.What is the NPV for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

c. What is the IRR for each project? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. a.

The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment. AZM Mini-SUV:

Cumulative cash flows Year 1 = $322,000 Cumulative cash flows Year 2 = $322,000 + 184,000

= $322,000 = $506,000

Payback period = 1 + $138,000/$184,000 Payback period = 1.75 years AZF Full-SUV: Cumulative cash flows Year 1 = $352,000 Cumulative cash flows Year 2 = $352,000 + 424,000 Cumulative cash flows Year 2 = $352,000 + 424,000 + 292,000

= $352,000 = $776,000 = $1,068,000

Payback period = 2 + $34,000/$292,000 Payback period = 2.12 years Since the AZM has a shorter payback period than the AZF, the company should choose the AZM. Remember the payback period does not necessarily rank projects correctly. b.

The NPV of each project is:

NPVAZM = –$460,000 + $322,000/1.09 + $184,000/1.092 + $152,000/1.093 NPVAZM = $107,653.85

NPVAZF = –$810,000 + $352,000/1.09 + $424,000/1.09 2 + $292,000/1.093 NPVAZF = $95,285.67

The NPV criteria implies we accept the AZM because it has the highest NPV. c.

The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR of the AZM is: 0 = –$460,000 + $322,000/(1 + IRR) + $184,000/(1 + IRR)2 + $152,000/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRRAZM = 23.84% And the IRR of the AZF is: 0 = –$810,000 + $352,000/(1 + IRR) + $424,000/(1 + IRR)2 + $292,000/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRRAZF = 15.66% The IRR criteria implies we accept the AZM because it has the highest IRR. Remember the IRR does not necessarily rank projects correctly.

Calculator Solution: b.

AZM CFo C01 F01 C02 F02 C03 F03 I = 9%

–$460,000 $322,000 1 $184,000 1 $152,000 1

AZF CFo C01 F01 C02 F02 C03 F03 I = 9%

–$810,000 $352,000 1 $424,000 1 $292,000 1

NPV CPT $107,653.85

NPV CPT $95,285.67

c.

AZM CFo C01 F01 C02 F02 C03 F03 IRR CPT 23.84%

–$460,000 $322,000 1 $184,000 1 $152,000 1

AZF CFo C01 F01 C02 F02 C03 F03 IRR CPT 15.66%

–$810,000 $352,000 1 $424,000 1 $292,000 1

Chapter 5, Question 3 An investment project has annual cash inflows of $3,800, $4,700, $5,900, and $5,100, and a discount rate of 14 percent. a.

b.

What is the discounted payback period for these cash flows if the initial cost is $6,500? (D o not round intermedi ate calculatio ns and round your answ er to 2 decimal places, e.g., 32.16.) What is the

c.

Explanation

discounted payback period for these cash flows if the initial cost is $8,600? (D o not round intermedi ate calculatio ns and round your answer to 2 decimal places, e.g., 32.16.) What is the discounted payback period for these cash flows if the initial cost is $11,600? ( Do not round intermedi ate calculatio ns and round your answer to 2 decimal places, e.g., 32.16.)

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. When we use discounted payback, we need to find the value of all cash flows today. The value today of the project cash flows for the first four years is: Value Value Value Value

today today today today

of of of of

Year Year Year Year

1 2 3 4

cash cash cash cash

flow flow flow flow

= = = =

$3,800/1.14 = $3,333.33 $4,700/1.142 = $3,616.50 $5,900/1.143 = $3,982.33 $5,100/1.144 = $3,019.61

To find the discounted payback, we use these values to find the payback period. The discounted first year cash flow is $3,333.33, so the discounted payback for an initial cost of $6,500 is: Discounted payback = 1 + ($6,500 – 3,333.33)/$3,616.50 Discounted payback = 1.88 years For an initial cost of $8,600, the discounted payback is: Discounted payback = 2 + ($8,600 – 3,333.33 – 3,616.50)/$3,982.33 Discounted payback = 2.41 years Notice the calculation of discounted payback. We know the payback period is between two and three years, so we subtract the discounted values of the Year 1 and Year 2 cash flows from the initial cost. This is the numerator, which is the discounted amount we still need to make to recover our initial investment. We divide this amount by the discounted amount we will earn in Year 3 to get the fractional portion of the discounted payback. If the initial cost is $11,600, the discounted payback is: Discounted payback = 3 + ($11,600 – 3,333.33 – 3,616.50 – 3,982.33)/ $3,019.61 Discounted payback = 3.22 years Chapter 5, Question 4 An investment project costs $10,000 and has annual cash flows of $2,930 for six years.

a.

b.

What is the discounted payback period if the discount rate is 0 percent? (En ter 0 if the project never pays back on a discounted payback basis. Do not round intermediat e calculations and round your answer to 2 decimal places, e.g., 32.16.) What is the discounted payback period if the discount rate is 5 percent? (En ter 0 if the project never pays back on a discounted payback basis. Do not round intermediat e calculations and round your answer to 2 decimal

places, e.g., 32.16.) What is the discounted payback period if the discount rate is 19 percent? (En ter 0 if the project never pays back on a discounted payback basis. Do not round intermediat e calculations and round your answer to 2 decimal places, e.g., 32.16.)

c.

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. To calculate the discounted payback, discount all future cash flows back to the present, and use these discounted cash flows to calculate the payback period. To find the fractional year, we divide the amount we need to make in the last year to pay back the project by the amount we will make. Doing so, we find:

R = 0%: 3 + ($1,210/$2,930) = 3.41 years Discounted payback = Regular payback = 3.41 years R = 5%: $2,930/1.05 + $2,930/1.052 + $2,930/1.053 = $7,979.12

$2,930/1.054 = $2,410.52 Discounted payback = 3 + ($10,000 – 7,979.12)/$2,410.52 Discounted payback = 3.84 years R= 19%:

$2,930/1.19 + $2,930/1.192 + $2,930/1.193 + $2,930/1.194 + $2,930/1.195 + $2,930/1.196 = $9,990.65 The project never pays back on a discounted payback basis.

Chapter 5, Question 5 Vital Silence, Inc., has a project with the following cash flows: Year 0 1 2 3

Cash Flow – 27,40 $ 0 11,40 0 14,40 0 10,40 0

The appropriate discount rate is 16 percent. What is the IRR for this project? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Should the firm accept the project? Accept Reject Explanation  

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is:

0 = C0 + C1/(1 + IRR) + C2/(1 + IRR)2 + C3/(1 + IRR)3 0 = –$27,400 + $11,400/(1 + IRR) + $14,400/(1 + IRR)2 + $10,400/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 15.53% Since the IRR is less than the required return we would reject the project. Calculator Solution:

CFo C01 F01 C02 F02 C03 F03

–$27,400 $11,400 1 $14,400 1 $10,400 1

IRR CPT 15.53%

Chapter 5, Question 6 Compute the internal rate of return for the cash flows of the following two projects. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Year 0 1 2 3

Project Project B A – 14,30 – 11,90 $ 0 $ 0 5,600 3,000 6,400 8,900 5,200 4,800

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this Project A is:

0 = C0 + C1/(1 + IRR) + C2/(1 + IRR)2 + C3/(1 + IRR)3 0 = –$14,300 + $5,600/(1 + IRR) + $6,400/(1 + IRR)2 + $5,200/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 9.95%

And the IRR for Project B is: 0 = C0 + C1/(1 + IRR) + C2/(1 + IRR)2 + C3/(1 + IRR)3 0 = –$11,900 + $3,000/(1 + IRR) + $8,900/(1 + IRR)2 + $4,800/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 17.78% Calculator Solution:

Project A CFo C01 F01 C02 F02 C03

–$14,300 $5,600 1 $6,400 1 $5,200

Project B CFo C01 F01 C02 F02 C03

–$11,900 $3,000 1 $8,900 1 $4,800

F03 IRR CPT 9.95%

1

F03 IRR CPT 17.78%

1

Chapter 5, Question 7 Solo Corp. is evaluating a project with the following cash flows: Year 0 1 2 3 4 5

Cash Flow –$ 28,900 11,100 13,800 15,700 12,800 – 9,300

The company uses a discount rate of 13 percent and a reinvestment rate of 6 percent on all of its projects. Calculate the MIRR of the project using the discounting approach. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Calculate the MIRR of the project using the reinvestment approach. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Calculate the MIRR of the project using the combination approach. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. With different discounting and reinvestment rates, we need to make sure to use the appropriate interest rate. The MIRR for the project with all three approaches is:

Discounting approach: In the discounting approach, we find the value of all cash outflows at Time 0, at the discount rate, while any cash inflows remain at the time at which they occur. So, discounting the cash outflows to Time 0, we find: Time 0 cash flow = –$28,900 – $9,300/1.135 Time 0 cash flow = –$33,947.67 So, the MIRR using the discounting approach is: 0 = –$33,947.67 + $11,100/(1 + MIRR) + $13,800/(1 + MIRR)2 + $15,700/(1 + MIRR)3 + $12,800/(1 + MIRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: MIRR = 20.22% Reinvestment approach: In the reinvestment approach, we find the future value of all cash flows, except the initial cash flow, at the end of the project using the reinvestment rate. So, reinvesting the cash flows to Time 5, we find: Time 5 cash flow = $11,100(1.064) + $13,800(1.063) + $15,700(1.062) + $12,800(1.06) – $9,300 Time 5 cash flow = $52,358.04 So, the MIRR using the discounting approach is: 0 = –$28,900 + $52,358.04/(1 + MIRR)5 $52,358.04/$28,900 = (1 + MIRR)5 MIRR = ($52,358.04/$28,900)1/5 – 1 MIRR = .1262, or 12.62% Combination approach: In the combination approach, we find the value of all cash outflows at Time 0 using the discount rate, and the value of all cash inflows at the end of the project using the reinvestment rate. So, the value of the cash flows is:

Time 0 cash flow = –$28,900 – $9,300/1.135 Time 0 cash flow = –$33,947.67 Time 5 cash flow = $11,100(1.064) + $13,800(1.063) + $15,700(1.062) + $12,800(1.06) Time 5 cash flow = $61,658.04 So, the MIRR using the discounting approach is: 0 = –$33,947.67 + $61,658.04/(1 + MIRR)5 $61,658.04/$33,947.67 = (1 + MIRR)5 MIRR = ($61,658.04/$33,947.67)1/5 – 1 MIRR = .1268, or 12.68% Chapter 5, Question 8 Solo Corp. is evaluating a project with the following cash flows: Year 0 1 2 3 4 5

Cash Flow –$ 29,600 11,800 14,500 16,400 13,500 – 10,000

The company uses an interest rate of 10 percent on all of its projects. Calculate the MIRR of the project using the discounting approach. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Calculate the MIRR of the project using the reinvestment approach. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Calculate the MIRR of the project using the combination approach. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. The MIRR for the project with all three approaches is: Discounting approach: In the discounting approach, we find the value of all negative cash outflows at Time 0, while any positive cash inflows remain at the time at which they occur. So, discounting the cash outflows to Time 0, we find: Time 0 cash flow = –$29,600 – $10,000/1.105 Time 0 cash flow = –$35,809.21 So, the MIRR using the discounting approach is: 0 = –$35,809.21 + $11,800/(1 + MIRR) + $14,500/(1 + MIRR)2 + $16,400/(1 + MIRR)3 + $13,500/(1 + MIRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find: MIRR = 20.13% Reinvestment approach: In the reinvestment approach, we find the future value of all cash flows, except the initial cash flow, at the end of the project. So, reinvesting the cash flows to Time 5, we find: Time 5 cash flow = $11,800(1.104) + $14,500(1.103) + $16,400(1.102) + $13,500(1.10) – $10,000 Tim...